One of the salient features of ultracold atomic systems is that they are intrinsically clean. Nevertheless, artificial impurities can be engineered in atomic systems, which allows one to investigate their effects. In this talk, I will discuss our recent work on the effects of a localized impurity potential on atomic Fermi gases. Such an impurity can be used to manipulate or probe exotic quantum phases of fermionic superfluids. For example, it can be exploited to create the FFLO state in a controlled manner or to realize Majorana edge state in a topological Ferm gas with Rashba spin-orbit coupling.
One of the salient features of ultracold atomic systems is that they are intrinsically clean. Nevertheless, artificial impurities can be engineered in atomic systems, which allows one to investigate their effects. In this talk, I will discuss our recent work on the effects of a localized impurity potential on atomic Fermi gases. Such an impurity can be used to manipulate or probe exotic quantum phases of fermionic superfluids. For example, it can be exploited to create the FFLO state in a controlled manner or to realize Majorana edge state in a topological Ferm gas with Rashba spin-orbit coupling.
Ultracold Fermi gas is an exciting field benefiting from atomic physics, optical physics and condensed matter physics. It covers many aspects of quantum mechanics. Here I introduce some of my work during my graduate study. We proposed an optical spectroscopic method based on electromagnetically-induced transparency (EIT) as a generic probing tool that provides valuable insights into the nature of Fermi paring in ultracold Fermi gases of two hyperfine states. This technique has the capability of allowing spectroscopic response to be determined in a nearly non-destructive manner and the whole spectrum may be obtained by scanning the probe laser frequency faster than the lifetime of the sample without re-preparing the atomic sample repeatedly. Both quasiparticle picture and pseudogap picture are constructed to facilitate the physical explanation of the pairing signature in the EIT spectra. Motivated by the prospect of realizing a Fermi gas of 40 K atoms with a synthetic non-Abelian gauge field, we investigated theoretically BEC-HCS crossover physics in the presence of a Rashba spin-orbit coupling in a system of two-component Fermi gas with and without a Zeeman field that breaks the population balance. A new bound state (Rashba pair) emerges because of the spin-orbit interaction. We studied the properties of Rashba pairs using a standard pair fluctuation theory. As the two-fold spin degeneracy is lifted by spin-orbit interaction, bound pairs with mixed singlet and triplet pairings (referred to as rashbons) emerge, leading to an anisotropic superfluid. We discussed in detail the experimental signatures for observing the condensation of Rashba pairs by calculating various physical observables which characterize the properties of the system and can be measured in experiment. The role of impurities as experimental probes in the detection of quantum material properties is well appreciated. Here we studied the effect of a single classical impurity in trapped ultracold Fermi superfluids. Although a non-magnetic impurity does not change macroscopic properties of s-wave Fermi superfluids, depending on its shape and strength, a magnetic impurity can induce single or multiple mid-gap bound states. The multiple mid-gap states could coincide with the development of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase within the superfluid. As an analog of the Scanning Tunneling Microscope, we proposed a modified radio frequency spectroscopic method to measure the focal density of states which can be employed to detect these states and other quantum phases of cold atoms. A key result of our self consistent Bogoliubov-de Gennes calculations is that a magnetic impurity can controllably induce an FFLO state at currently accessible experimental parameters.
Chiral superfluidity in ultracold Fermi gases represents a fascinating frontier in condensed matter physics, offering a pristine platform for exploring exotic quantum phases with topological properties. This paper provides a comprehensive review of the theoretical underpinnings and potential experimental realizations of chiral superfluids when ultracold Fermi gases are subjected to artificial gauge fields. We begin by introducing the concept of artificial gauge fields, detailing how they can be engineered using laser-atom interactions to impart synthetic spin-orbit coupling and break time-reversal symmetry, thereby creating conditions conducive to chiral order. We then delve into the microscopic theory of chiral pairing, particularly focusing on p-wave and p+ip superfluid states, which are intrinsically chiral and support topologically protected edge modes, such as Majorana fermions. The methodology section outlines the theoretical tools employed, including mean-field BCS theory and Bogoliubov-de Gennes equations, to predict the phase diagrams and spectroscopic signatures of these exotic states. We discuss the effects of varying interaction strengths, gauge field parameters, and trapping potentials on the emergence and stability of chiral phases. The potential for experimental detection through rf spectroscopy, noise correlations, and direct imaging of vortex cores is also addressed. Our findings underscore the significant potential of ultracold atomic systems as quantum simulators for unraveling the mysteries of topological phases, with profound implications for fundamental physics and quantum information science.
The role of impurities as experimental probes in the detection of quantum material properties is well appreciated. Here we study the effect of a single classical magnetic impurity in trapped ultracold Fermi superfluids. Depending on its shape and strength, a magnetic impurity can induce single or multiple midgap bound states in a superfluid Fermi gas. The multiple midgap states could coincide with the development of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase within the superfluid. As an analog of the scanning tunneling microsope, we propose a modified rf spectroscopic method to measure the local density of states which can be employed to detect these states and other quantum phases of cold atoms. A key result of our self-consistent Bogoliubov-de Gennes calculations is that a magnetic impurity can controllably induce an FFLO state at currently accessible experimental parameters.
In cold atom experiments, we have tools to create spin dependent optical potential, which gives us the possibility to achieve classical magnetic impurity in cold atom systems. Here we study the physics of magnetic impurity. A localized magnetic impurity can induce a mid-gap bound state, the Yu-Shiba state, in superfluid Fermi gas. We propose a modified RF spectroscopy to measure the local density of states, as a cold-atom analog of STM, which may be used to detect Yu-Shiba state. In addition, magnetic impurity can locally induce population imbalance in the system, potentially providing a method to realize FFLO-like state in a controlled way. We demonstrate such a possibility by solving the self-consist Bogoliubov-de Gennes equations.
Advances in experiments on dilute ultracold atomic gases have given us access to highly tunable quantum systems. In particular, there have been substantial improvements in achieving different kinds of interaction between atoms. As a result, utracold atomic gases oer an ideal platform to simulate many-body phenomena in condensed matter physics, and engineer other novel phenomena that are a result of the exotic interactions produced between atoms. In this dissertation, I present a series of studies that explore the physics of dilute ultracold atomic gases in different settings. In each setting, I explore a different form of the inter-particle interaction. Motivated by experiments which induce artificial spin-orbit coupling for cold fermions, I explore this system in my first project. In this project, I propose a method to perform universal quantum computation using the excitations of interacting spin-orbit coupled fermions, in which effective p-wave interactions lead to the formation of a topological superfluid. Motivated by experiments which explore the physics of exotic interactions between atoms trapped inside optical cavities, I explore this system in a second project. I calculate the phase diagram of lattice bosons trapped in an optical cavity, where the cavity modes mediates effective global range checkerboard interactions between the atoms. I compare this phase diagram with one that was recently measured experimentally. In two other projects, I explore quantum simulation of condensed matter phenomena due to spin-dependent interactions between particles. I propose a method to produce tunable spin-dependent interactions between atoms, using an optical Feshbach resonance. In one project, I use these spin-dependent interactions in an ultracold Bose-Fermi system, and propose a method to produce the Kondo model. I propose an experiment to directly observe the Kondo effect in this system. In another project, I propose using lattice bosons with a large hyperfine spin, which have Feshbach-induced spin-dependent interactions, to produce a quantum dimer model. I propose an experiment to detect the ground state in this system. In a final project, I develop tools to simulate the dynamics of fermionic superfluids in which fermions interact via a short-range interaction.
We investigate the stabilization of topological Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases, with a specific emphasis on the intraband FFLO phase, in a one-dimensional (1D) Fermi gas subjected to an external magnetic field. This research highlights the crucial role of the interplay between Rashba spin-orbit coupling (RSOC) and Dresselhaus spin-orbit coupling (DSOC). Employing a Fermi-Hubbard model alongside the density matrix renormalization group (DMRG) method, we examine the combined effects of RSOC and DSOC on these exotic superfluid phases, taking into account attractive fermionic interactions. Our principal finding reveals that while RSOC primarily stabilizes conventional zero-momentum pairing, DSOC performs a distinct and crucial role in selectively stabilizing the intraband FFLO phase. This stabilization is achieved by enhancing spin polarization within a single helicity band and suppressing interband coherence, thereby facilitating the formation of finite-momentum FFLO pairs within the same band and resulting in the emergence of a topologically nontrivial superfluid. This targeted control of intraband FFLO pairing paves the way for new strategies in the manipulation of superfluid phases in spin-orbit coupled systems and offers essential insights for experimental realizations in ultracold atomic gases, with implications for topological quantum computing and Majorana fermions.